Question

Describe an algorithm that shows that the following problem is decidable: given two regular expressionsR1andR2, is L(R1) =L(R2)? Hint: use Kleene’s theorem that relates regular expressions and finite automata

Answer 1

We use the 2 properties here:-

1. Given a regular expression R, then by Kleene's theorem, there always exist a DFA M corresponding to R such that L(R) =L(M).

2. Given 2 DFAs M1 and M2, the problem of finding L(M1) = L(M2) is decidable.

Following is the decidable algorithm:-

1. Create DFA M1 and M2 corresponding to R1 and R2 respectively.

2. If L(M1) = L(M2) then accept else reject.

Hence the problem L(R1) = L(R2) is decidable.